Angular and self-consistency contributions to the Sternheimer hexadecapole antishielding factorη∞

Linked-cluster many-body perturbation theory has been used to calculate the Sternheimer hexadecapole antishielding factor ${\eta }_{\infty }$ in ${\mathrm{Pr}}^{3+}$. This parameter is a measure of enhancement of a possible nuclear electric hexadecapole (16-pole) moment due to polarization of the core electrons in an atom or ion. Large and predominant contributions due to the angular mode of excitations neglected in earlier works have been found. Self-consistency contributions to ${\eta }_{\infty }$ are found to be small (about 3%), similar to those in the quadrupole antishielding factor ${\gamma }_{\infty }$. These contributions in the case of quadrupole polarizability ${\alpha }_q$ and the crystal-field shielding parameter ${\sigma }_2$ in ${\mathrm{Pr}}^{3+}$ were found to be larger (about 17% but of opposite sign in both cases).